scholarly journals Reliability Analysis of the Proportional Mean Residual Life Order

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
M. Kayid ◽  
S. Izadkhah ◽  
H. Alhalees
Keyword(s):  
Residual Life ◽  
Stochastic Order ◽  
Mean Residual Life ◽  
New Order ◽  
Mean Residual Life Function ◽  
New Class ◽  
Mean Residual Life Order ◽  
Life Distributions ◽  
The Mean ◽  
Life Function

The concept of mean residual life plays an important role in reliability and life testing. In this paper, we introduce and study a new stochastic order called proportional mean residual life order. Several characterizations and preservation properties of the new order under some reliability operations are discussed. As a consequence, a new class of life distributions is introduced on the basis of the anti-star-shaped property of the mean residual life function. We study some reliability properties and some characterizations of this class and provide some examples of interest in reliability.

MEAN RESIDUAL LIFE FUNCTION FOR ADDITIVE AND MULTIPLICATIVE HAZARD RATE MODELS

2015 ◽  
Vol 30 (2) ◽  
pp. 281-297 ◽  
Author(s):  
Ramesh C. Gupta
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Turning Points ◽  
Sufficient Conditions ◽  
Mean Residual Life ◽  
Residual Life Function ◽  
Mean Residual Life Function ◽  
Hazard Rate Models ◽  
The Mean ◽  
Life Function

This paper deals with the mean residual life function (MRLF) and its monotonicity in the case of additive and multiplicative hazard rate models. It is shown that additive (multiplicative) hazard rate does not imply reduced (proportional) MRLF and vice versa. Necessary and sufficient conditions are obtained for the two models to hold simultaneously. In the case of non-monotonic failure rates, the location of the turning points of the MRLF is investigated in both the cases. The case of random additive and multiplicative hazard rate is also studied. The monotonicity of the mean residual life is studied along with the location of the turning points. Examples are provided to illustrate the results.

scholarly journals Preservation of the mean residual life order for coherent and mixed systems

2019 ◽  
Vol 56 (01) ◽  
pp. 153-173 ◽  
Author(s):  
Bo H. Lindqvist ◽  
Francisco J. Samaniego ◽  
Nana Wang
Keyword(s):  
Residual Life ◽  
Stochastic Order ◽  
Mean Residual Life ◽  
Coherent System ◽  
Hazard Rate Order ◽  
Stochastic Orderings ◽  
Mean Residual Life Order ◽  
The Mean ◽  
Point Of Departure ◽  
Mixed Systems

AbstractThe signature of a coherent system has been studied extensively in the recent literature. Signatures are particularly useful in the comparison of coherent or mixed systems under a variety of stochastic orderings. Also, certain signature-based closure and preservation theorems have been established. For example, it is now well known that certain stochastic orderings are preserved from signatures to system lifetimes when components have independent and identical distributions. This applies to the likelihood ratio order, the hazard rate order, and the stochastic order. The point of departure of the present paper is the question of whether or not a similar preservation result will hold for the mean residual life order. A counterexample is provided which shows that the answer is negative. Classes of distributions for the component lifetimes for which the latter implication holds are then derived. Connections to the theory of order statistics are also considered.

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